Static or Quasi Static loading

Quasistatic loading refers to loading where inertial effects are negligible. This means time and inertial mass are irrelevant.
It also means - if you have got your densities wring in your material properties for FEA. Dont worry the results wont change ;)

Shown below is a youtube video that I found online that shows real life quasi static tests

Guess the video helps understand what a quasi static test is.

Explain Hourglassing?

The standard numerical integration (e.g. 2x2 Gaussian quadrature for a bilinear quad, 2x2x2 for a trilinear hexa) has some flaws when combined with incompressible material. The  displacements in the mesh are orders of magnitude smaller than in the reality. This is called volumetric locking. To overcome this overstiffening we use reduced integration (for 4-node quads and 8-node hexas 1 integration point in the middle). Reduced integration solves the volumetric locking both in theory and tests. However now there is a new problem: consider a 4-node quad. Move the nodes on one edge towards each other, and the other edge in the opposite direction, on both sides with the same amount. The element is now deformed to the shape of a trapezium, but the integration point (where your starins are measured) which is in the middle of the element does not feel any of this deformation. Neither the vertical nor the horizontal direction changed the length and angle of the mid lines. That means there is now a deformation which produces no strains, hence no forces to resist. This pattern can grow unbounded, and easily destroy the whole simulation. This deformation pattern is called hourglass mode, or zero energy mode, or kinematic mode etc. We have to stabilize the element against hourglassing and the energy used to counter this is called hourglass energy.

Below is a youtube video that I found which shows hourglassing in an Ls-Dyna deck.

Hope that helped!

Why do we prefer to have Solid elements in Foams with Elform 1 instead of 2 ? - Lsdyna related

Elform 2 is a fully integrated model, so there is a tendency for negative volume in soft materials due to crushing . Elform 1 is a single integration model. As the integration point is in the middle of the element, even if the crossing over of nodes of one edge over the other may cause a physical negative volume but for all calculations it is possible that the centre node of the element is still on the +ve side and hence negative volume will be avoided. In case of excessive compression or warping, this may also become a negative volume.